粘弹性树脂基三维编织复合材料的热膨胀性能研究

首先利用均匀化理论并结合有限元法研究了三维编织复合材料的粘弹性效应,根据松弛模量的计算结果研究了材料热膨胀系数随时间的变化关系,在此基础上,给出了编织结构和工艺参数(编织角、纤维体积比)对材料初始热膨胀系数的影响规律,计算结果与实验值吻合较好。本文工作为深入研究三维编织复合材料的热粘弹性能提供了基础。     

无网格方法在平面粘弹性力学问题中的应用

本文综合应用无网格方法(EFGM)、线性粘弹性与弹性力学之间的对应原理,Laplace变换和逆变换等方法求解了拟静态平面弹性和粘弹性力学问题。首先,利用Laplace变换和逆变换推导了平面问题的粘弹性本构关系,建立了拟静态粘弹性平面问题的边值问题;其次,利用粘弹性与弹性力学之间的对应原理得到了Laplace变换域中平面问题的基本方程,在Laplace变换域中建立了相应的泛函,并得到了用无网格方法离散的控制方程;同时,求解了几个拟静态弹性和粘弹性平面问题,给出了它们的表达式和数值结果;最后,采用Laplace逆变换和数值逆变换,得到了粘弹性力学平面问题在物理空间中的解,并比较了由解析解和无网格数值方法所得到的数值结果,可以看到它们是非常吻合的。说明本文方法的正确性和有效性。     

黏弹性功能梯度材料裂纹问题的有限元方法

针对组分材料体积含量任意分布的黏弹性功能梯度材料裂纹问题建立有限元分析途径. 通过Laplace变换,将黏弹性问题转化到象空间中求解,基于反映材料非均匀的梯度单元和裂纹尖端奇异特性的奇异单元计算象空间中的位移、应力和应变场,应用虚拟裂纹闭合方法得到应变能释放率,分别由应力和应变能释放率确定应力强度因子. 给出这些断裂参量在物理空间和象空间之间的对应关系,由数值逆变换求出其在物理空间的相应值. 文中分析两端均匀受拉的黏弹性边裂纹板条,首先针对松弛模量表示为空间函数和时间函数乘积的特殊梯度材料进行计算,结合对应原理验证方法的有效性. 然后分析组分材料体积含量具有任意梯度分布的情形,由Mori-Tanaka方法预测象空间中的等效松弛模量. 计算结果表明,蠕变加载条件下,应变能释放率随时间增加,其增大程度与黏弹性组分材料体积含量相关. 由于梯度材料的非均匀黏弹性性质,产生应力重新分布,导致应力强度因子随时间变化,其变化范围与组分材料的体积含量分布方式有关.     

树脂基三维编织复合材料粘弹性性能的有限元分析

根据材料的细观结构,采用APDL语言分别建立了纤维束和三维编织复合材料两级单胞的参数化几何模型;推导了Prony级数表示的树脂粘弹性本构方程,对模型进行了组分材料参数设置;对纤维束单胞模型进行扫掠式网格划分,对三维编织复合材料单胞模型进行线-面-体式网格划分;对两级单胞模型均施加合理的边界条件,使单胞边界上的位移满足周期性和连续性。以有限元模型为基础,计算了三维编织复合材料的粘弹性能,并给出了材料粘弹性效应随工艺参数变化的规律。计算结果表明:三维编织复合材料编织方向的粘弹性效应随编织角的增大而增强,随纤维体积比的增大而减弱。该结果与已有实验结论一致。     

粘弹性胶层中Ⅰ型裂纹的动态扩展

研究粘弹性胶层中Griffith裂纹在Ⅰ型载荷作用下,裂纹尖端动态应力强度因子和能量释放率的时间响应.首先,利用积分变换方法,推导出粘弹性层的控制方程组;其次,引入位错密度函数,并结合边界条件和界面连接条件,导出反映裂纹尖端奇异性的Cauchy型奇异积分方程组,然后,应用Chebyshev正交多项式化奇异积分方程组为代数方程组,并采用Schmidt方法对其数值求解,最后,经过Laplace逆变换,求得动态应力强度因子和能量释放率的时间响应.通过对材料参数的讨论,得到动应力强度因子和能量释放率随剪切松驰参量的减小而增大,随膨胀松弛参量的减小而减小,弹性参数对其影响较小.     

SHPB实验中粘弹性试件内部应力波的传播

建立描述SHPB实验中线性粘弹性试件内部应力波传播的控制方程组,根据试件两端与入射杆及透射杆接触的应力波特征关系给出耦合边界条件.对方程组和定解条件进行Laplace变换,求得试件内部应力在变换域像函数的表达式.采用数值反变换技术进行反Laplace变换,获得试件两端的应力时程曲线.对现有的固定Tal-bot反变换算法进行改进:将入射波像函数分解为基本部分和延迟部分,利用固定Talbot算法对基本部分入射波作用下的波动问题求解,其他部分的解通过延迟定理得到,最终解为两部分的叠加.采用这种改进算法得到的不同入射波下粘弹性试件的内部应力解与传统的基于特征线数值模拟方法的结果吻合.在此基础上探讨了粘弹性试件的几何参数和材料本构参数对透射波波形的影响.     

应用自洽方法预测沥青混合料的蠕变行为

将沥青混合料看作是由沥青砂和粗骨料组成的两相复合材料,提出了应用自洽方法预测沥青混合料粘弹性性能的一般思路.采用四参量流变模型描述沥青砂的粘弹性能,通过 Laplace 变换将时间域的粘弹性问题转化为变换域的线弹性问题,然后经 Laplace 逆变换将变换域的解转化到时间域.利用不同温度、不同应力水平下沥青砂的单轴压缩蠕变实验,拟合四参量流变模型参数,预测了沥青混合料在不同温度和不同应力水平下的蠕变曲线,并与实验结果进行了比较,发现蠕变的早期阶段预测值与实验值基本符合.最后进一步分析了温度、应力水平对沥青混合料蠕变行为的影响.     

纤维加强复合材料的总体粘弹性响应

在某些纤维增强复合材料(FRC)中使用金属或高分子聚合物作为基体材料。在高温等情况下,这类材料具有明显的粘弹性特性。本文采用Riemann—Liouville形式的分数阶导数模型描述基体的粘弹性特性。通过渐近均匀化方法给出了预测FRC整体三维本构关系的解析表达式。给出了应用于基体具有Makris粘弹性关系的具体形式。以圆截面纤维正方形排列的情形为例,给出了等效模量随纤维体积比的变化曲线。结果说明,这类复合材料仍具有粘弹性特性,其整体粘弹性本构关系的弹性部分综合了纤维弹性和基体弹性的贡献,粘性部分来自基体粘性的贡献,复合材料具有和基体相同的粘性系数和分数阶。为分析微结构特征对整体特性的贡献,须求解两类局部问题。可以看出,在整体的等效模量中包含了局部变形的贡献,局部变形增加了复合材料的耦合刚度。     

粘弹性结构动力稳定性分析的谐波平衡法

本文分析了线粘弹性结构的长期动力稳定特性。设材料具积分型本构关系，且其松弛模量能用Prony级数描述，将微分-积分型控制方程化成微分型方程，应用谐波平衡法确定动力稳定区域，着重讨论了材料参数及系统振动频率对动力稳定区域的影响发现该类粘弹性结构具有与一般阻尼系统不同的动力稳定特性。文中也将系统平衡法直接应用于微分-积分型控制方程，忽略卷积积分运算后产生的随时间衰减的非谐波项来得到决定动力稳定边界的特征方程，并对两种应用所得结果进行了比较。     

考虑损伤的粘弹性梁的纯弯曲

根据粘弹性损伤理论,分析了带损伤粘弹性矩形梁在受纯弯曲时损伤对应力的影响,得到了在Laplace变换域内损伤场和应力场的分布．利用Laplace数值逆变换,分别得到了损伤弹性梁和损伤粘弹性梁的最大应力和最大损伤值,分析了材料的粘性对梁内应力和损伤的影响。     

Three-dimensional continuum analysis for a unidirectional composite with a broken fiber

The three-dimensional problem of a periodic unidirectional composite with a penny-shaped crack traversing one of the fibers is analyzed by the continuum equations of elasticity. The solution of the crack problem is represented by a superposition of weighted unit normal displacement jump solutions, everyone of which forms a Green’s function. The Green’s functions for the unbounded periodic composite are obtained by the combined use of the representative cell method and the higher-order theory. The representative cell method, based on the triple discrete Fourier transform, allows the reduction of the problem of an infinite domain to a problem of a finite one in the transform space. This problem is solved by the higher-order theory according to which the transformed displacement vector is expressed by a second order expansion in terms of local coordinates, in conjunction with the equilibrium equations and the relevant boundary conditions. The actual elastic field is obtained by a numerical evaluation of the inverse transform. The accuracy of the suggested approach is verified by a comparison with the exact analytical solution for a penny-shaped crack embedded in a homogeneous medium. Results for a unidirectional composite with a broken fiber are given for various fiber volume fractions and fiber-to-matrix stiffness ratios. It is shown that for certain parameter combinations the use of the average stress in the fiber, as it is employed in the framework of the shear lag approach, for the prediction of composite’s strength, leads to an over estimation. To this end, the concept of “point stress concentration factor” is introduced to characterize the strength of the composite with a broken fiber. Several generalizations of the proposed approach are offered.     

The effective properties of composites with fiber-end cracks

The paper describes use of self-consistent finite element method (SCFEM) for predicting effective properties of fiber composite with partially debonded interface. The effective longitudinal Young's modulus and shear modulus for unidirectional fiber reinforced composites with fiber-end cracks are calculated. Numerical results show that the effective properties are considerably influenced by the fiber-end cracks. The effects of microstructural parameters, such as fiber volume fraction, modulus ratio of the constituents and fiber aspect, on the effective properties of the composites were discussed. The project supported by the National Natural Science Foundation of China     

Simulation of fiber reinforced composite materials mold filling process and mechanical properties analysis

A dynamic simulation of fiber reinforced composite materials mold filling process with double inlets is presented based on the gas–solid–liquid model proposed by Yang et al. [B.X. Yang, J. Ouyang, J. Tao, C.T. Liu, Modeling and simulation of fiber reinforced polymer mold filling process by level set method, CMES – Computer Modeling in Engineering and Sciences 63 (3) (2010) 191–222]. Numerical results show that the fibers far away from the melt interface are in skin-core-skin structure, while those near the interface are almost parallel to the arc of the interface. When the two streams of melts meet, the weld line will be formed, where the orientation of fibers is perpendicular to the flow direction. The orientation of fibers of the numerical result shows well agreement with the experimental results. Finally, the mechanical properties of fiber reinforced composite materials are analyzed. The composite materials with skin-core-skin structure are regarded as laminated orthogonal plywood and the elastic modulus, the shear modulus and Poisson’s ratio are predicted under different slenderness ratios and fiber volume fractions.     

X状Z向碳pin增强泡沫夹层结构剪切刚度预报

综合考虑了面板对横向增强Z-pin的不同约束情况,结合空间网架结构和等效夹杂方法,提出了X状Z-pins增强泡沫夹层结构剪切刚度的预报模型,经实际计算后与已有的实验值和有限元模拟值比较,证明该方法具有足够的工程精度.计算表明,X状Z-pins能大幅度地提高泡沫夹层结构的剪切刚度,并具有良好的可设计性,可以通过改变Z-pin材料,Z-pin的体积分数、角度、直径等参数改变其力学性能.其中,Z-pin体积分数越大、拉伸模量越高、直径越大,Z-pins增强泡沫夹层结构的剪切刚度越高.     

A nonlinear constitutive model of unidirectional natural fiber reinforced composites considering moisture absorption

Moisture absorption in natural fiber reinforced composites causes remarkable degradation of mechanical properties. A nonlinear constitutive model is proposed to study the effect of the water uptake on the mechanical properties of unidirectional natural fiber reinforced composites. Accompanying the water absorption in the composites, there are several irreversible thermodynamic processes such as fiber degradation and interface damage. The energy dissipation induced by these processes is described by an internal variable, and two degradation parameters representing interface damage and fiber degradation are introduced to reflect the modulus reduction of the composite. Particularly, the model is used to derive the evolution of elastic moduli influenced by the moisture absorption. The predictions from the present model show a good agreement with experiment results of sisal fiber unidirectional reinforced composites.     

梯度密度黏弹性材料的波传播研究

梯度密度黏弹性材料中波的传播比较复杂。为了研究其在冲击载荷作用下黏弹性响应特征,基于控制方程的Euler形式,利用Laplace变换,得到了这种材料中的波传播规律的一个理论公式;并据此分析了双层周期性黏弹性介质中的应力情况。选择具有梯度密度特性的钛-硼化钛（Ti-TiB₂）材料和碳纤维树脂材料,采用不同的叠合方向和方式,利用分离式霍普金森压杆（split Hopkinson pressure bar,SHPB）加载装置进行了动态冲击实验,并用三波法对得到的实验结果进行处理。同时,采用数值Laplace逆变换方法,结合SHPB测得的入射波与透射波数据,使用推导的理论公式计算出理论解,并与实验结果进行了比较。结果表明:（1）梯度钛-硼化钛材料由于内界面和叠层界面的存在,表现出一定的黏性特性;单层Ti-TiB₂材料的计算结果和三波法分析得到的结果基本一致,双层Ti-TiB₂材料叠合后的计算结果与三波法分析结果存在一定的差异。（2）双层碳纤维树脂材料表现出较强的黏弹性特征,应力波的衰减幅度较大,三波法分析结果与该材料的冲击性能有较大的差异。由此可知,无论是细微观结构特征产生的黏性,还是材料本身的黏性,对材料动力学行为的影响都不可忽略。。     

Effective properties of a linear viscoelastic composite

The relaxation moduli of a composite are determined. The relaxation of its components is described by various few-parameter kernels: Mittag-Leffler functions of different orders and Rzhanitsyn kernel. It is assumed that the composite components are made of model materials with volume relaxation. The Laplace transform and fractional rational approximation are used to develop an algorithm for reducing the relaxation functions of the composite to one class (series of decreasing exponents or exponents of fractional order). The relaxation moduli of a unidirectionally reinforced composite are determined as an example     

Saint-Venant problem of three-dimensional linear viscoelasticity in the Hamiltonian system

The traditional Saint-Venant problem of three-dimensional viscoelasticity is discussed under the Hamiltonia system with the use of the Laplace integral transformation, and the original problem is transformed into finding eigenvalues and eigenvectors of the Hamiltonia operator matrix. Since local effect near the boundary is usually neglected, all solutions of Saint-Venant problems can be obtained directly by the combinations of zero eigenvectors. Moreover, the adjoint relationships of the symplectic orthogonality of zero eigenvectors in the Laplace domain are generalized to the time domain. Therefore the problem can be discussed directly in the eigenvector space of the time domain, and the iterative application of Laplace transformation is not needed. Simply by applying the adjoint relationships of the symplectic orthogonality, an effective method for boundary condition is given. Based on this method, some typical examples are discussed, in which the whole character of total creep and relaxation of viscoelasticity is clearly revealed.     

Numerical simulation of fiber reinforced composite materials––two procedures

In this work, two methodologies for the analysis of unidirectional fiber reinforced composite materials are presented.The first methodology used is a generalized anisotropic large strains elasto-plastic constitutive model for the analysis of multiphase materials. It is based on the mixing theory of basic substance. It is the manager of the several constitutive laws of the different compounds and it allows to consider the interaction between the compounds of the composite materials. In fiber reinforced composite materials, the constitutive behavior of the matrix is isotropic, whereas the fiber is considered orthotropic. So, one of the constitutive model used in the mixing theory needs to consider this characteristic. The non-linear anisotropic theory showed in this work is a generalization of the classic isotropic plasticity theory (A Continuum Constitutive Model to Simulate the Mechanical Behavior of Composite Materials, PhD Thesis, Universidad Politécnica de Cataluña, 2000). It is based in a one-to-one transformation of the stress and strain spaces by means of a four rank tensor.The second methodology used is based on the homogenization theory. This theory divided the composite material problem into two scales: macroscopic and microscopic scale. In macroscopic level the composite material is assuming as a homogeneous material, whereas in microscopic level a unit volume called cell represents the composite (Tratamiento Numérico de Materiales Compuestos Mediante la teorı́ de Homogeneización, PhD Thesis, Universidad Politécnica, de Cataluña 2001). This formulation presents a new viewpoint of the homogenization theory in which can be found the equations that relate both scales. The solution is obtained using a coupled parallel code based on the finite elements method for each scale problem.